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Schaefer–Krasnoselskii Fixed Point Theorems Using a Usual Measure of Weak Noncompactness

Mohammadi, Sajjad | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 47471 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Ranjbar Motlagh, Alireza
  7. Abstract:
  8. In this thesis, we present some extension of Burton and Kirk fixed point theorem for the sum of two nonlinear operators, which one of them is compact and the other one is strict contraction; and we investigate the existence of fixed point where these two operators don’t need to be weakly continuous. Next, we will check the necessity of some conditions, like being strict contraction or compactness, in some specific Banach spaces, such as reflective spaces or Banach spaces equipped with uniformly convex norm.Finally, we analysis the existence of the solution for integral equations in L1 space by using the expressed theorems
  9. Keywords:
  10. Krasnoselski Fixed Point Theorem ; Nonlinear Integral Equation ; Weak Noncompactness Measure

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